Question

Answer the following questions:

1) In what ways can you show the probability distribution of a situation?

2) What does E(X) calculate? Can you rely on this value always?

3) How can we determine whether or a not a situation represents a uniform distribution?

4) How can we tell whether or a not situation is considered "fair game"? Provide an example within your explaination.

5) Provide an example of a situation (that has not be been mentioned) that illustrates binomial distribution.

6) When creating the probability distribution histograms for binomial distributions, how do the histograms tend to look like?

7) How are binomial distributions similar to hypergeometric distributions?

8) How are binomial distributions different from hypergeometric distributions?

9) Where have you seen the probability formula for hypergeometric distributions before (refer to past lessons)?

Answer 1

1) In order to find the probability distribution of a situation we have to find probability of each occurance. And then write the ordered pair with first entry the value and the second entry the probability of the value.

2) E(X) calculates the expected value of the random variable X. It's the value which one expects after the random experiment is performed.

We make most of the inferences based on E(X) and it's also the unbiased estimator for population mean.

3) A situation represents uniform distribution if each of the occurance have same chance of happening. That is probability of each outcome is same, like in the case id rolling a six sided die once. Then each of the outcomes 1 to 6 have same probability of occurance that is

4) When we toss a coin there are two possible outcomes Head, or Tail each with same probability of occurance that is 0.50.

If there is a coin where head has probability of occurance 0.7, then in this case the coin is not fair.

So we say if an outcome of an experiment has the likelihood same as what is expected than such a case we say game is fair. Otherwise not.

5) We say a random variable follows Binomial distribution if number if trials is finite, there are two outcomes of each trial, the probability of success is constant in each case.

Example Let's take a sample of 10 Students where we are interested in knowing how many have solved a particular problem, if any student has p probability of solving the problem.

Then it's a binomial distribution with 20 trials and p probability of success.

6) The histogram looks symmetry about the mean, with a bell shape.

That is like normal distribution curve.